Why -50% Needs +100% to Recover
You lost -50%, so a +50% rise should get you back to breakeven, right? But in reality, it takes a +100% rise to return to your principal. Let's find out why this 'unfair math' arises.
Loss and gain have different 'reference points'
Suppose you have $740. From here, -50% leaves $370. Now, for this $370 to become $740 again, how much does it need to rise?
Going from $370 to $740 is 'doubling'—that is, +100%. The reason it's +100% and not +50% is simple. The loss of -50% is calculated based on 'the original $740,' while the recovery of +100% is calculated based on 'the remaining $370.'
When a loss occurs, our money is already in a reduced state. Since it has to rise again based on that reduced amount, you always need a larger % than the % you lost.
The formula for the return needed to recover
If we call the drawdown D (e.g., -50% is 0.5), the return needed to recover the principal is calculated as follows.
Required return = D ÷ (1 − D)
Plugging in -50%: 0.5 ÷ (1 − 0.5) = 0.5 ÷ 0.5 = 1.0, that is, +100%. This formula shows that the larger the drawdown, the required recovery return grows 'with acceleration.'
Required recovery return by drawdown: -10% → +11.1%, -20% → +25%, -25% → +33.3%, -30% → about +43%, -50% → +100%, -75% → +300%, -90% → +900%. (Sources: Bogleheads, Investopedia-family calculators, and many others cross-checked)
The 'time to recover' that history proved
This asymmetry is not a story inside a calculator but something repeated in real markets.
The Nasdaq Composite Index peaked at 5,048 points in March 2000, then plunged about -78% to its 2002 low. To recover -78%, the required return is a whopping about +350%. In reality, it surpassed the 2000 peak again in April 2015, which took about 15 years.
The S&P 500 also fell about -57% from its peak during the 2007–2009 financial crisis, and recovered its previous peak in 2013, which took about 4 years. The deeper the drawdown, the greater both the return required to recover and the time it takes.
Figures differ slightly across sources, so they're written as ranges/approximations. The S&P 500's 2007–2009 drawdown is reported at about -56.8% to -57% depending on the source.
So what should you know
The lesson this formula gives is that 'avoiding a big loss in the first place is far easier than recovering from it.' -20% recovers with +25%, but -50% requires +100%, and -80% requires +400%. When the drawdown doubles, the recovery burden jumps not twofold but several-fold.
That said, this doesn't mean 'always cut losses' or 'sell at the peak.' Rather, it becomes a basis for deciding in advance—before investing—how much to diversify your assets and how much drawdown you can withstand. Only those who start out knowing the drawdown they can endure can get through a crash.
Frequently Asked Questions
Q. So is recovery impossible at -100%?
Yes. Plugging D=1 (-100%) into the formula D ÷ (1 − D) makes the denominator 0, so the calculation doesn't hold. When an asset's value becomes 0, no matter how high the % rises afterward, it's only multiplied by 0, so it can't be reversed. This is why the delisting of an individual stock is frightening, and why diversification matters.
Q. Are the 'return' and 'time' needed to recover different?
They're different. The required return is pure arithmetic (-50% needs +100%), but the time it takes for that return to actually be filled varies greatly from a few months to over a decade depending on market conditions. The COVID crash (about -34%) recovered in about 5 months, but the Nasdaq dot-com collapse took about 15 years.
Q. Can I ignore small losses?
It's true that the smaller the loss, the smaller the recovery burden. -10% recovers with just +11.1%. But if losses pile up repeatedly, they eventually act like one big drawdown. Costs like fees, taxes, and exchange rates also quietly enlarge the drawdown, so even a minus that looks small should be viewed from a cumulative perspective.
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📋 Results are based on historical data; past returns do not guarantee future returns.
📋 This service is provided for educational purposes to help you understand investing, not as investment advice.